Module 5: Physical chemistry & transition elements
Chapter 18: Rates of reactions
Orders, rate equations and rate constants
Rate of reaction
𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑟𝑒𝑎𝑐𝑡𝑒𝑑/𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛
● 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 = 𝑡𝑖𝑚𝑒
= 𝑡𝑖𝑚𝑒
● In concentration, units of rate of reaction is mol dm-3 s-1
● Notation: reaction A -> [A] (concentration of A)
Order of reaction
● Changing concentration proportionally changes rate of reaction
● rate ∝ [A]n - power is order of reaction for that reactant
● Different reactants can have different orders and each may affect rate in different ways
● Zero order:
○ rate ∝ [A]0 so -x graph for conc-time graph
○ Concentration of reactant has no effect on rate - x0 = 1
● First order:
○ rate ∝ [A]1 so 1/x graph for conc-time graph
○ Concentration of reactant has linear - x1 = x
● Second order:
○ rate ∝ [A]2 so 1/x2 graph for conc-time graph
○ Concentration of reactant is quadratic - x2
Rate equation and rate constant
● Gives relationship between concentrations of reactants and reaction rate
𝑚 𝑛
● Rate equation: 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 = 𝑘[𝐴] [𝐵]
● Overall order = m + n
● Rate constant k: proportionality constant - number that converts between
rate of reaction and concentration and orders
● Units of k found by rearranging equation to make k subject then
cancelling out units
Concentration-time graphs
Monitoring rate continuously
● Concentration-time graphs can be plotted from continuous measurements taken during
course of reaction (continuous monitoring)
● So far, we have learnt to monitor by gas collection or by mass loss - not all reactions have gas
produced
Monitoring with colorimeter
● Reaction may change colour as reactants react
● In colorimeter, wavelength of light passing through coloured solution
controlled using filter then amount of light absorbed by solution is
measured
● Filter chosen such that it is complementary colour to colour being absorbed by reaction
Concentration-time graphs
● Gradient of concentration-time graph is rate of reaction
● Order with respect to reactant can be deduced from shape of
concentration-time graph
● Zero order: straight line with negative gradient as reaction rate doesn’t change at all during
reaction, gradient = k
, ● First order: downward curve with decreasing gradient (reaction is slowing), half-life constant
and k can be found using this
● Second order: steeper than first order but tailing off more slowly
Half life
● Half life t1/2: time taken for half of reactant to be used up - exponential decay
𝑙𝑛 2 𝑙𝑛 2
● 𝑘 = ℎ𝑎𝑙𝑓 𝑙𝑖𝑓𝑒
(𝑘 = 𝑡1/2
)
● Zero order has decreasing half life, first order has constant, second order has increasing
Rate-concentration graphs and initial rates
Rate-concentration graphs
● Can be plotted from measurements of rate of reaction at different concentrations
● Offer direct link between rate and concentration in rate equation
● Zero order: rate = k so y-intercept = k
● First order: rate ∝ k[A] so gradient = k
● Second order: rate ∝ k[A]2 so have to draw rate-concentration2 graph to get gradient k
Initial rates method
● Initial rate: instantaneous rate at start of reaction when t = 0 - found by gradient of tangent at t
= 0 on concentration-time graph
● Clock reaction: time from start of experiment is measured for visual change to be observed
● Provided no significant change in rate during this time, can be assumed average rate of
reaction = initial rate = 1/t
● Iodine clock:
○ Aqueous iodine is orange-brown
○ Starch usually added as it forms intense dark blue-black coloured complex
○ Time from start of reaction and appearance of colour can be measured
● Accuracy:
○ Longer time = lower value than actual value as gradient gets less steep
○ Reasonably accurate provided <15% of reaction has occurred
Rate-determining step
Multi-step reactions
● Reaction mechanism: series of steps that make up overall reaction
● Rate-determining step: slowest step in sequence
● Rate equation only includes reacting species involved in rate-determining step
● Orders in rate equation match number of species involved in rate-determining step
● Rate-determining step provides important evidence in supporting or rejecting proposed
reaction mechanism
Examples:
●
●
Rate constants and temperature
Temperature
● As temperature increases, rate increases and k will increase
● Usually every 10oC rise doubles rate constant so doubles rate of reaction
● Increasing temperature shifts Boltzmann distribution to right, increasing proportion of particles
that exceed activation energy Ea
, ● As temperature increases, particles move faster and collide more frequently - relatively small
increase compared to shift in Boltzmann distribution
Arrhenius equation
−𝐸𝑎
● 𝑘 = 𝐴𝑒 𝑅𝑇 - A: pre-exponential factor (frequency factor), R: gas constant, T: temperature
(kelvin), must be in joules not kilojoules
● Shows relationship between temperature and rate constant
● Exponential factor represents proportion of particles that exceed activation energy and have
sufficient energy for reaction to take place
● Pre-exponential term A: frequency of collisions with correct orientation which has negligible
increase with small temperature increases
Taking logs of Arrhenius
𝐸𝑎 𝐸𝑎 1
● 𝑙𝑛 𝑘 =− 𝑅𝑇
+ 𝑙𝑛 𝐴, where 𝑙𝑛 𝑘 = 𝑦, − 𝑅
= 𝑚, 𝑇
= 𝑥, 𝑙𝑛 𝐴 = 𝑐
● Used to find A and Ea
Chapter 19: Equilibrium
Equilibrium constant Kc
Kc
● Equilibrium constant for equilibrium system in terms of equilibrium concentrations of species
present at equilibrium
𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜 𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜
[𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝐴] [𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝐵]
● 𝐾𝑐 = 𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜 𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜
[𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡 𝐴] [𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡 𝐵]
● Units found by cancelling out units from top and bottom
Equilibria
● Homogeneous: all species have same state
● Heterogeneous: not all species have same state - only include (g) or (aq) in Kc calculation
Calculating Kc example:
●
Equilibrium constant Kp
Kp
● Easier to use pressure than concentration in gases
● Hence Kp instead of Kc - both are still proportional to each other
𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜 𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜
𝑝(𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝐴) 𝑝(𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝐵)
● 𝐾𝑝 = 𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜 𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜
𝑝(𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡 𝐴) 𝑝(𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡 𝐵)
● Units can be Pa, kPa or atm but must be same for all
Mole fractions
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝐴
● 𝑚𝑜𝑙𝑒 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑥(𝐴) = 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 𝑖𝑛 𝑔𝑎𝑠 𝑚𝑖𝑥𝑡𝑢𝑟𝑒
● Sum of mole fractions = 1
Partial pressure
● Contribution gas makes towards total pressure
● 𝑝𝑎𝑟𝑡𝑖𝑎𝑙 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 = 𝑚𝑜𝑙𝑒 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝐴 × 𝑡𝑜𝑡𝑎𝑙 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 (𝑝(𝐴) = 𝑥(𝐴) × 𝑃)
● Sum of partial pressures = total pressure
Controlling equilibrium position
Equilibrium constant
● K < 1: equilibrium in favour of reactants
, ● K = 1: equilibrium halfway between reactants and products
● K > 1: equilibrium in favour of products
● At set temperature, K is constant and doesn’t change despite modifications to concentration,
pressure or presence of catalyst - only temperature can change K
Temperature
● Depends on whether forward reaction is exothermic or endothermic
● Exothermic reactions:
○ Equilibrium constant decreases with increasing temperature, shifting equilibrium
position to left and decreasing equilibrium yield of products
○ This is because Kp decreases as temperature increases so partial pressure of
products must decrease while reactants must increase, shifting equilibrium to left
● Endothermic reactions:
○ Equilibrium constant increases with increasing temperature, shifting equilibrium
position to right and increasing equilibrium yield of products
○ This is because Kp increases as temperature increases so partial pressure of
products must increase while reactants must decrease, shifting equilibrium to right
● Same logic with Kc - instead of partial pressures, concentrations are changed
Concentration and pressure
● Kc doesn’t change by concentration or pressure
● Changes in concentration and pressure shift equilibrium position to match Kc or Kp
● Increase in concentration of reactants shifts equilibrium position to right, decreasing
concentration of reactants and increasing concentration of products
● Increase in pressure shifts equilibrium position to side with fewer moles
Catalysts
● Affect rate of reaction but not position of equilibrium
● Speeds up forward and reverse reactions by same factor - equilibrium reached faster
Chapter 20: Acids, bases and pH
Bronsted-Lowry acids and bases
Acid and base
● Bronsted-Lowry acid: proton donor
● Bronsted-Lowry base: proton acceptor
Conjugate acid-base pairs
● Contains 2 species that can be interconverted by transfer of proton
+ −
● Example: 𝐻𝐶𝑙 ⇌ 𝐻 + 𝐶𝑙 (equilibrium arrow despite HCl strong acid so equilibrium to right)
○ In forward direction, HCl releases proton to form its conjugate base Cl-
○ In reverse direction, Cl- accepts proton to form its conjugate acid HCl
+ −
● 𝐻 + 𝑂𝐻 ⇌ 𝐻2𝑂: OH- is a base (accepts H+) while H2O is an acid (donates H+)
+ −
● 𝐻𝐶𝑙 + 𝐻2𝑂 ⇌ 𝐻3𝑂 + 𝐶𝑙 : H2O, Cl- is a base while HCl, H3O+ is an acid
● H3O+ (hydronium) active acid ingredient in any aqueous acid
Monobasic, dibasic and tribasic acids
● Number of hydrogen ions in acid than can be replaced per molecule in acid-base reaction
● Mono: 1, di: 2, tri: 3
H+ and acid reactions
● H+ is active species of acid in acid reactions
● Hydrogen in acid is replaced by metal or ammonium ions to form salt
● Salt: chemical compound of positively and negatively charged ions
● Salt naming: alkali acid
● Ionic equation will show neutralisation of H+ ions by OH- ions to form neutral H2O
Chapter 18: Rates of reactions
Orders, rate equations and rate constants
Rate of reaction
𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑟𝑒𝑎𝑐𝑡𝑒𝑑/𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛
● 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 = 𝑡𝑖𝑚𝑒
= 𝑡𝑖𝑚𝑒
● In concentration, units of rate of reaction is mol dm-3 s-1
● Notation: reaction A -> [A] (concentration of A)
Order of reaction
● Changing concentration proportionally changes rate of reaction
● rate ∝ [A]n - power is order of reaction for that reactant
● Different reactants can have different orders and each may affect rate in different ways
● Zero order:
○ rate ∝ [A]0 so -x graph for conc-time graph
○ Concentration of reactant has no effect on rate - x0 = 1
● First order:
○ rate ∝ [A]1 so 1/x graph for conc-time graph
○ Concentration of reactant has linear - x1 = x
● Second order:
○ rate ∝ [A]2 so 1/x2 graph for conc-time graph
○ Concentration of reactant is quadratic - x2
Rate equation and rate constant
● Gives relationship between concentrations of reactants and reaction rate
𝑚 𝑛
● Rate equation: 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 = 𝑘[𝐴] [𝐵]
● Overall order = m + n
● Rate constant k: proportionality constant - number that converts between
rate of reaction and concentration and orders
● Units of k found by rearranging equation to make k subject then
cancelling out units
Concentration-time graphs
Monitoring rate continuously
● Concentration-time graphs can be plotted from continuous measurements taken during
course of reaction (continuous monitoring)
● So far, we have learnt to monitor by gas collection or by mass loss - not all reactions have gas
produced
Monitoring with colorimeter
● Reaction may change colour as reactants react
● In colorimeter, wavelength of light passing through coloured solution
controlled using filter then amount of light absorbed by solution is
measured
● Filter chosen such that it is complementary colour to colour being absorbed by reaction
Concentration-time graphs
● Gradient of concentration-time graph is rate of reaction
● Order with respect to reactant can be deduced from shape of
concentration-time graph
● Zero order: straight line with negative gradient as reaction rate doesn’t change at all during
reaction, gradient = k
, ● First order: downward curve with decreasing gradient (reaction is slowing), half-life constant
and k can be found using this
● Second order: steeper than first order but tailing off more slowly
Half life
● Half life t1/2: time taken for half of reactant to be used up - exponential decay
𝑙𝑛 2 𝑙𝑛 2
● 𝑘 = ℎ𝑎𝑙𝑓 𝑙𝑖𝑓𝑒
(𝑘 = 𝑡1/2
)
● Zero order has decreasing half life, first order has constant, second order has increasing
Rate-concentration graphs and initial rates
Rate-concentration graphs
● Can be plotted from measurements of rate of reaction at different concentrations
● Offer direct link between rate and concentration in rate equation
● Zero order: rate = k so y-intercept = k
● First order: rate ∝ k[A] so gradient = k
● Second order: rate ∝ k[A]2 so have to draw rate-concentration2 graph to get gradient k
Initial rates method
● Initial rate: instantaneous rate at start of reaction when t = 0 - found by gradient of tangent at t
= 0 on concentration-time graph
● Clock reaction: time from start of experiment is measured for visual change to be observed
● Provided no significant change in rate during this time, can be assumed average rate of
reaction = initial rate = 1/t
● Iodine clock:
○ Aqueous iodine is orange-brown
○ Starch usually added as it forms intense dark blue-black coloured complex
○ Time from start of reaction and appearance of colour can be measured
● Accuracy:
○ Longer time = lower value than actual value as gradient gets less steep
○ Reasonably accurate provided <15% of reaction has occurred
Rate-determining step
Multi-step reactions
● Reaction mechanism: series of steps that make up overall reaction
● Rate-determining step: slowest step in sequence
● Rate equation only includes reacting species involved in rate-determining step
● Orders in rate equation match number of species involved in rate-determining step
● Rate-determining step provides important evidence in supporting or rejecting proposed
reaction mechanism
Examples:
●
●
Rate constants and temperature
Temperature
● As temperature increases, rate increases and k will increase
● Usually every 10oC rise doubles rate constant so doubles rate of reaction
● Increasing temperature shifts Boltzmann distribution to right, increasing proportion of particles
that exceed activation energy Ea
, ● As temperature increases, particles move faster and collide more frequently - relatively small
increase compared to shift in Boltzmann distribution
Arrhenius equation
−𝐸𝑎
● 𝑘 = 𝐴𝑒 𝑅𝑇 - A: pre-exponential factor (frequency factor), R: gas constant, T: temperature
(kelvin), must be in joules not kilojoules
● Shows relationship between temperature and rate constant
● Exponential factor represents proportion of particles that exceed activation energy and have
sufficient energy for reaction to take place
● Pre-exponential term A: frequency of collisions with correct orientation which has negligible
increase with small temperature increases
Taking logs of Arrhenius
𝐸𝑎 𝐸𝑎 1
● 𝑙𝑛 𝑘 =− 𝑅𝑇
+ 𝑙𝑛 𝐴, where 𝑙𝑛 𝑘 = 𝑦, − 𝑅
= 𝑚, 𝑇
= 𝑥, 𝑙𝑛 𝐴 = 𝑐
● Used to find A and Ea
Chapter 19: Equilibrium
Equilibrium constant Kc
Kc
● Equilibrium constant for equilibrium system in terms of equilibrium concentrations of species
present at equilibrium
𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜 𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜
[𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝐴] [𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝐵]
● 𝐾𝑐 = 𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜 𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜
[𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡 𝐴] [𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡 𝐵]
● Units found by cancelling out units from top and bottom
Equilibria
● Homogeneous: all species have same state
● Heterogeneous: not all species have same state - only include (g) or (aq) in Kc calculation
Calculating Kc example:
●
Equilibrium constant Kp
Kp
● Easier to use pressure than concentration in gases
● Hence Kp instead of Kc - both are still proportional to each other
𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜 𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜
𝑝(𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝐴) 𝑝(𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝐵)
● 𝐾𝑝 = 𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜 𝑚𝑜𝑙𝑒 𝑟𝑎𝑡𝑖𝑜
𝑝(𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡 𝐴) 𝑝(𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡 𝐵)
● Units can be Pa, kPa or atm but must be same for all
Mole fractions
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝐴
● 𝑚𝑜𝑙𝑒 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑥(𝐴) = 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 𝑖𝑛 𝑔𝑎𝑠 𝑚𝑖𝑥𝑡𝑢𝑟𝑒
● Sum of mole fractions = 1
Partial pressure
● Contribution gas makes towards total pressure
● 𝑝𝑎𝑟𝑡𝑖𝑎𝑙 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 = 𝑚𝑜𝑙𝑒 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝐴 × 𝑡𝑜𝑡𝑎𝑙 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 (𝑝(𝐴) = 𝑥(𝐴) × 𝑃)
● Sum of partial pressures = total pressure
Controlling equilibrium position
Equilibrium constant
● K < 1: equilibrium in favour of reactants
, ● K = 1: equilibrium halfway between reactants and products
● K > 1: equilibrium in favour of products
● At set temperature, K is constant and doesn’t change despite modifications to concentration,
pressure or presence of catalyst - only temperature can change K
Temperature
● Depends on whether forward reaction is exothermic or endothermic
● Exothermic reactions:
○ Equilibrium constant decreases with increasing temperature, shifting equilibrium
position to left and decreasing equilibrium yield of products
○ This is because Kp decreases as temperature increases so partial pressure of
products must decrease while reactants must increase, shifting equilibrium to left
● Endothermic reactions:
○ Equilibrium constant increases with increasing temperature, shifting equilibrium
position to right and increasing equilibrium yield of products
○ This is because Kp increases as temperature increases so partial pressure of
products must increase while reactants must decrease, shifting equilibrium to right
● Same logic with Kc - instead of partial pressures, concentrations are changed
Concentration and pressure
● Kc doesn’t change by concentration or pressure
● Changes in concentration and pressure shift equilibrium position to match Kc or Kp
● Increase in concentration of reactants shifts equilibrium position to right, decreasing
concentration of reactants and increasing concentration of products
● Increase in pressure shifts equilibrium position to side with fewer moles
Catalysts
● Affect rate of reaction but not position of equilibrium
● Speeds up forward and reverse reactions by same factor - equilibrium reached faster
Chapter 20: Acids, bases and pH
Bronsted-Lowry acids and bases
Acid and base
● Bronsted-Lowry acid: proton donor
● Bronsted-Lowry base: proton acceptor
Conjugate acid-base pairs
● Contains 2 species that can be interconverted by transfer of proton
+ −
● Example: 𝐻𝐶𝑙 ⇌ 𝐻 + 𝐶𝑙 (equilibrium arrow despite HCl strong acid so equilibrium to right)
○ In forward direction, HCl releases proton to form its conjugate base Cl-
○ In reverse direction, Cl- accepts proton to form its conjugate acid HCl
+ −
● 𝐻 + 𝑂𝐻 ⇌ 𝐻2𝑂: OH- is a base (accepts H+) while H2O is an acid (donates H+)
+ −
● 𝐻𝐶𝑙 + 𝐻2𝑂 ⇌ 𝐻3𝑂 + 𝐶𝑙 : H2O, Cl- is a base while HCl, H3O+ is an acid
● H3O+ (hydronium) active acid ingredient in any aqueous acid
Monobasic, dibasic and tribasic acids
● Number of hydrogen ions in acid than can be replaced per molecule in acid-base reaction
● Mono: 1, di: 2, tri: 3
H+ and acid reactions
● H+ is active species of acid in acid reactions
● Hydrogen in acid is replaced by metal or ammonium ions to form salt
● Salt: chemical compound of positively and negatively charged ions
● Salt naming: alkali acid
● Ionic equation will show neutralisation of H+ ions by OH- ions to form neutral H2O
